Reciprocal Convexity to reverse the Jensen Inequality
Jensen’s inequality is a powerful tool often used in mathematical derivations and analyses. It states that for a convex function \(f(x)\) and an arbitrary random variable \(X\) we have the following upper bound: \[ f\left(\E X\right) \le \E f\left(X\right) \]
However, oftentimes we want the inequality to work in the other direction, to give a lower bound. In this post I’ll outline one possible approach to this.